You have n programs p1, ..., pn with size m1, ..., mn MB (mega bytes). You have a disk that can store up to W MB.W is less than the total size of the programs. You are asked to use a dynamic programming solution to store the programs onto the disk so as to maximize the disk space utilization. In other words, you want to find a subset of programs such that its total size is maximized but has to be less than C.
Define U[i,w] as the maximum disk utilization of a disk with capacity w MB and programs p1,...,pi to be selected for storing it on the disk. Write a recurrence for U[i,w] and identify the boundary condition.